You have 20 minutes…

You have 20 minutes… • Pick up everything you need off the back desk to finish the practice test from yesterday. • Make sure your scan tron has your name on it. • Check your Unit 5 homework also!

Trigonometry Mary Lauren Willis Sydnee Wilcher Kaylee S. Kayla S.

Periodic Functions • Periodic Function- repeats a pattern of y-values at regular intervals • Period- horizontal length of one cycle • Cycle-one complete pattern • Amplitude- height; measures variations in the function values • ½(Maximum-Minimum)

1). Highlight one cycle 2). Period? 3). Amplitude? 4). Graph the midline Amplitude deals with the ___ value. Period deals with the ___ value.

Unit Circle

Examples • Convert measure to radians or degrees: • 260° • -220° • 5π/4 • -6π/5

How to graph trigonometric functions • y= asin b(x-c)+d • y= acos b(x-c)+d • a= amplitude • If negative- flip • b= period • c= horizontal shift • d= vertical shift

Sine and cosine graphs Graph sinΘ and cosΘ Period= 2π Amplitude=1 ~amplitude and period correspond~

Shifting sine and cosine graphs Shift y=sin(x) π/2 units right Equation:

transformations Domain: Range: Amplitude: Period: Phase Shift: Vertical Slide: y=2cosΘ

Graph tangent Domain: Range: Amplitude: Period: Zeroes: y=tanΘ

Trigonometric equations • a impacts the amplitude of the graph • b alters the period • A change in c causes a horizontal shift • When c is positve(x-c), the graph shifts right • When c is negative(x+c), the graph shifts left • A change in d causes a vertical shift • When d is positive, the graph shifts up • When d is negative, the graph shifts down

Trig identities- Reciprocal identities

Trig identities- Pythagorean identities

Verify tan²Θ- sin²Θ= tan²Θsin²Θ

Simplify (1+cot²Θ)(sec²Θ-1)

Unit 6 Questions

You have 20 minutes…